Chapter 8.6, Problem 20P

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection or by (6.18), (6.23) or $(6.24).$ Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form [see (6.26) and the discussion after $(6.15)]$.

$y^{\prime \prime }+4y^{\prime }+8y=30e^{-x/2}\cos 5x/2$